Let t be real number such that `t^2=at+b` for some positive integers a and b. Then forany choice of positive integers a and b.`t^3` is never equal to

If a and b are positive integers then

How many positive integers b have the property that log_(b)729 is a positive integer ?

How many positive integers b have the property that log_(b)729 is a positive integer ?

If a-b=4 and a^2+b^2=40 , where a and b are positive integers, then a^3+b^3 is equal to

If a and b are positive integers such that a^(b)=125 , then (a-b)^(a+b-4) is equal to

Statement 1: Let A ,B be two square matrices of the same order such that A B=B A ,A^m=O ,n dB^n=O for some positive integers m ,n , then there exists a positive integer r such that (A+B)^r=Odot Statement 2: If A B=B A then (A+B)^r can be expanded as binomial expansion.

Show that the square of any positive odd integer is of the form 4t+ 1, for some integer t.

a and b are positive integers such that a^3 - b^2 is a prime number. Then a^2 - b^2=

If a and b are positive integers such that a^(2)-b^(4)=2009, find a+b